| Title:
|
Cubic splines with minimal norm (English) |
| Author:
|
Kobza, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
285-295 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Natural cubic interpolatory splines are known to have a minimal $L_2$-norm of its second derivative on the $C^2$ (or $W^2_2)$ class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite $C^1$ splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed. (English) |
| Keyword:
|
cubic interpolatory spline |
| Keyword:
|
minimal norm interpolation |
| MSC:
|
41A15 |
| MSC:
|
65D05 |
| MSC:
|
65D07 |
| idZBL:
|
Zbl 1090.65012 |
| idMR:
|
MR1900515 |
| DOI:
|
10.1023/A:1021749621862 |
| . |
| Date available:
|
2009-09-22T18:10:17Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134498 |
| . |
| Reference:
|
[1] A. Bjorck: Numerical Methods for Least Squares Problems.SIAM, Philadelphia, 1996. MR 1386889 |
| Reference:
|
[2] C. Boor: A Practical Guide to Splines.Springer-Verlag, New York-Heidelberg-Berlin, 1978. Zbl 0406.41003, MR 0507062 |
| Reference:
|
[3] L. Brugnano, D. Trigiante: Solving Differential Equations by Multistep. Initial and Boundary Value Methods.Gordon and Breach, London, 1998. MR 1673796 |
| Reference:
|
[4] R. Fletcher: Practical Methods of Optimization.Wiley, Chichester, 1993. MR 1867781 |
| Reference:
|
[5] J. Kobza: Splajny. Textbook.VUP, Olomouc, 1993. (Czech) |
| Reference:
|
[6] J. Kobza: Computing solutions of linear difference equations.In: Proceedings of the XIIIth Summer School Software and Algorithms of Numerical Mathematics, Nečtiny 1999, I. Marek (ed.), University of West Bohemia, Plzeň, 1999, pp. 157–172. |
| Reference:
|
[7] J. S. Zavjalov, B. I. Kvasov and V. L. Miroschnichenko: Methods of Spline Functions.Nauka, Moscow, 1980. (Russian) MR 0614595 |
| . |
